Main results
- (potential) settler mortality/settlements \(\Rightarrow\) early institutions \(\Rightarrow\) current institutions
PSCI 2270 - Week 10
Department of Political Science, Vanderbilt University
November 9, 2023
Project Updates
What if we cannopt randomize?
Instrumental Variables: Colonial origins
Regression Discontinuity: Finding close elections
Differences-in-differences: Tabloid meida in UK
Key idea: Randomization of the treatment makes the treatment and control groups “identical” on average
The two groups are expected to be similar in terms of all characteristics (both observed and unobserved)
If we want to study effects of factor \(X\) on \(Y\) we would ideally want to run an experiment
Uses observational data, but is better than correlation
What is the difference between random and as-if random?
Theories on cholera have two hypotheses of transmission: water or air
As-if random event:
| Water Supply Company | Number of Houses | Deaths From Cholera | Cholera Deaths per 10,000 Houses |
|---|---|---|---|
| Southwark and Vauxhall | 40,046 | 1,263 | 315 |
| Lambeth | 26,107 | 98 | 37 |
| Rest of London | 256,423 | 1,422 | 59 |
Was the exposure actually random?
Random: Lotteries related to politically relevant processes; Timing of events
As-if random: Borders and historical events
Summary:
Question: Why are some countries rich and some are poor? (\(Y\))
Hypothesis: Extractive institutions (\(X\)) are persistent and can affect long-term development
Searching for as-if random assignment:
What is an instrument: Some factor that affects our main independent variable (early institutions) but is unlikely to affect our main outcome (current development) directly
Instrument in Acemoglu, Johnson, and Robinson (2001):
Instead of simple correlation we use two-stage procedure (2SLS)
To prove that instrument is valid researcher needs:
Different sources of data (some predicted mortality, some direct measures) \(\Rightarrow\) Selection bias
Data on troops (some in barracks and some on campaign) \(\Rightarrow\) Selection bias
Why use data on troops at all if it is not the same as settlers \(\Rightarrow\) Measurement validity
Can settlers affect current levels of development not through institutions? \(\Rightarrow\) Violation of excludability
Introduction (2 pages)
Theory and Hypotheses (1-2 pages)
Research design (5-7 pages)
Appendix (😵💫 pages)
“As-if” random events often need to use adjustments to standard difference-in-means analyses
Regression with covariates: Control for possible confounders \(\Leftarrow\) Football affects elections
Instrumental variables: Use before and after treatment comparison within the same unit \(\Leftarrow\) Colonial origins
Regression Discontinuity (RDD): Use some naturally occurring discontinuity (e.g. taxation, border, election, football match win) to compare units around it \(\Leftarrow\) Extremists win primaries
Differences-in-Differences (DiD): Compare trends between treated and untreated units even if we know there might be differences between them \(\Leftarrow\) Tabloid media in UK
New solutions:
\(\Leftarrow\) RDD design: “forcing variable” on X axis and outcome of interest on Y axis
\(\Rightarrow\) DiD design: trends in outcomes between “treated” and “control” units before and after the event (and also projects what the “treated” units “untreated” potential outcomes would be)
Try to guess what are the major issues to consider are with either of those designs?
Summary:
Question: Is having more ideologically extreme candidates good or bad for the party/voters?
Hypothesis: More extreme party candidate today \(\Rightarrow\) lower chances of winning today \(\Rightarrow\) lower representation today / lower future incumbency advantage
Searching for as-if random assignment:
We need to look at the elections that were almost won and just won by extremists \(\Rightarrow\) Extremists vote share in primaries is forcing variable
Two questions:
\[ \color{#98971a}{Y_{ipt}} = \beta_{0} + \color{#458588}{\beta_{1}} \color{#d65d0e}{\text{Extremist Primary Win}_{ipt}} + f(V_{ipt}) + \epsilon_{ipt} \]
\(i\) is usually unit within one time period, \(t\) is usually time, \(p\) - party
Outcome of interest: vote share/victory/roll-call voting score
Treatment indicator: whether extremist wins contested primaries (vs moderate) and proceeds to national elections
RDD treatment estimate
What is \(f(V_{ipt})\)?
What are possible issues here?
Summary:
Question: What are the long-term consequences of exposure to tabloid media?
Hypothesis: Boycott of tabloid media \(\Rightarrow\) less exposure to coverage of this tabloid media by youth and working class \(\Rightarrow\) less support for leaving EU \(\Rightarrow\) Less voting to leave EU during 2016 Referendum
Searching for as-if random assignment:
While Boycott is a shock to media consumption it is not random and is compound treatment (affects many things at once)
Two questions:
\[ \color{#98971a}{\text{leavingEU}_{i,c,t}} = \alpha_{c} + \gamma_{t} + \color{#458588}{\delta_{\text{DID}}} \color{#d65d0e}{T_{c,t}} + \varepsilon_{i,c,t} \]
\(i\) as before is unit (respondent) in one time period, \(t\) is as before time, \(c\) - constituency
Outcome of interest: answer to question about support for leaving EU
Treatment indicator: whether respondent resides in constituency in Merseyside after the Boycott start
DiD treatment estimate
What is \(\alpha_{c}\) and \(\gamma_{t}\)?
What are possible issues here?
There is an ordering of designs in terms of how persuasively they avoid confounding:
The order is often reversed if we are concerned about naturalistic setting/long-term effects/Logistical costs: